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Popular >

derivative of 4x(x^2-4)

Solution

\frac{d}{d x} (4 x (x^{2} - 4))

Solution

4 (3 x^{2} - 4)

Solution steps

\frac{d}{d x} (4 x (x^{2} - 4))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x (x^{2} - 4))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} - 4

= 4 (\frac{d x}{d x} (x^{2} - 4) + \frac{d}{d x} (x^{2} - 4) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} - 4) = 2 x

= 4 (1 \cdot (x^{2} - 4) + 2 xx)

Simplify

4 (1 \cdot (x^{2} - 4) + 2 xx) : 4 (3 x^{2} - 4)

= 4 (3 x^{2} - 4)

Popular Examples

integral of 1/(2x^2-x)

\int \frac{1}{2 x ^{2} - x} d x

derivative of f(x)=5x-7 derivative of

f (x) = 5 x - 7

derivative of x^3sqrt(2x-1)

\frac{d}{d x} (x^{3} 2 x - 1)

derivative of x^3-x^2-2x

\frac{d}{d x} (x^{3} - x^{2} - 2 x)

tangent of y=-9x^2,\at x=8 tangent of

y = - 9 x^{2}, at x = 8

Frequently Asked Questions (FAQ)

What is the derivative of 4x(x^2-4) ?
The derivative of 4x(x^2-4) is 4(3x^2-4)
What is the first derivative of 4x(x^2-4) ?
The first derivative of 4x(x^2-4) is 4(3x^2-4)